Mathematics — CBSE Class 10 board question

(A) 36

Given: $x = 6\sin A$, $y = 6\cos A$. So $x^2 + y^2 = 36\sin^2 A + 36\cos^2 A = 36(\sin^2 A + \cos^2 A) = 36 \times 1 = \mathbf{36}$.

Source: Introduction to Trigonometry, Section 8.5 (Identity: $\sin^2 A + \cos^2 A = 1$)

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• First simplify: $\frac{x}{3} = 2\sin A \Rightarrow x = 6\sin A$; similarly $y = 6\cos A$.
• Then $x^2 + y^2 = 36\sin^2 A + 36\cos^2 A = 36(\sin^2 A + \cos^2 A)$.
• Apply the fundamental identity $\sin^2 A + \cos^2 A = 1$ to get 36.
• The key skill tested: algebraic substitution + Pythagorean identity. Always look to form $\sin^2 A + \cos^2 A$ when you see both sin and cos of the same angle.